Bayesian Neural Learning via Langevin Dynamics for Chaotic Time Series Prediction

Although neural networks have been very promising tools for chaotic time series prediction, they lack methodology for uncertainty quantification. Bayesian inference using Markov Chain MontCarlo (MCMC) algorithms have been popular for uncertainty quantification for linear and non-linear models. Langevin dynamics refer to a class of MCMC algorithms that incorporate gradients with Gaussian noise in parameter updates. In the case of neural networks, the parameter updates refer to the weights of the network. We apply Langevin dynamics in neural networks for chaotic time series prediction. The results show that the proposed method improves the MCMC random-walk algorithm for majority of the problems considered. In particular, it gave much better performance for the real-world problems that featured noise.